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摘要翻译：
本文研究了由pitt和shephard(1999)提出的辅助粒子滤波(APF)产生的加权样本的渐近性质。除了建立光滑粒子估计的中心极限定理外，我们还得到了有限粒子样本容量下光滑粒子估计的Lp误差和偏差的界。通过考察CLT渐近方差的递推公式，我们确定了在算法的单次迭代中渐近方差增加最小的第一级重要性权重。根据这些发现，我们讨论并通过几个例子证明了如何改进有源滤波器算法。
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英文标题：
《On the auxiliary particle filter》
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作者：
Randal Douc (CMAP), Eric Moulines (LTCI), Jimmy Olsson (LTCI)
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by pitt and shephard (1999). Besides establishing a central limit theorem (CLT) for smoothed particle estimates, we also derive bounds on the Lp error and bias of the same for a finite particle sample size. By examining the recursive formula for the asymptotic variance of the CLT we identify first-stage importance weights for which the increase of asymptotic variance at a single iteration of the algorithm is minimal. In the light of these findings, we discuss and demonstrate on several examples how the APF algorithm can be improved.
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PDF链接：
https://arxiv.org/pdf/709.3448
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